Animating a boolean operation gives inconsequent results
I only looked at your BoolTest01.blend file.
First I applied the the Modifier on the &quot;Water&quot; object that had the &quot;B_Box halving&quot; as a target object. Then I applied the rotation of the &quot;Water&quot; object: 3D viewport &gt; Object &gt; Apply &gt; Rotation. After that the glitching seemed to have disappeared.
Hope that (also) works for you.
EDIT:
I've seen some strange things happening in your third file. Among others, on opening the file the &quot;Water&quot; and the &quot;Box halving&quot; behaving as one object when trying to select the Water. And getting a kind of &quot;can't assign value&quot; message (don't remember it exactly and didn't record it) when trying to apply a Boolean modifier at some point.
Also tried a bunch of things to fix your problem. Making the cylinder have an all quads topology and reapplying the Boolean modifiers in various ways.
I was almost out of ideas, but i found another fix that works for me. It is not ideal, but it might be adequate.
I believe the perfect aligning of the side of the &quot;Box halving&quot; and the height edges exactly in the middle of the &quot;Water&quot; cylinder might be responsible for confusing the boolean operation.
So i moved the center of the cylinder slightly to the side (1 mm according to the MeasureIt Tools; hardly noticeable) and that made the glitching disappear.

Again, i hope that (also) works for you